To improve the performance of IHT, Zhao [1]}, [2]} recently proposed the optimal \(k\) -thresholding technique which stresses that thresholding of a vector should be performed simultaneously with objective function reduction in the course of iterations.
Replacing \({\cal H}_k\)  by the optimal \(k\) -thresholding operator \({\cal Z}^{\#}_k\)  in (REF ) leads to the following iterative optimal \(k\) -thresholding scheme:
\(x^{p+1} = {\cal Z}^{\#}_k \left(x^p - \lambda \nabla f(x^p) \right).\) 
